The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields.

Includes a number of original contributions to the study of linear and non-linear Hyperbolic PDE's Provides a comprehensive, detailed review of singularities in fluid models and a survey on recent developments in detonation theory Offers new ideas on several topics, like geometric optics, elasticity, planar detonations, solvability for PDE's and Weyl's formula for eigenvalues

Autorentext

Ferruccio Colombini has been a Professor of Mathematical Analysis at the University of Pisa since 1986. His main interests are the theory of linear and nonlinear hyperbolic PDE's.

Daniele Del Santo is Professor of Mathematical Analysis at the University of Trieste. He works in the field of hyperbolic and parabolic operators with non-smooth coefficients.

David Lannes is CNRS Research Director at the Institut de Mathématiques de Bordeaux. He works on nonlinear PDEs and has a strong interest in applications to oceanography.

Inhalt

1 Amplitude equations for weakly nonlinear surface waves in variational problems.- 2 Global weak solutions of PDEs for compressible media: A compactness criterion to cover new physical situations.- 3 Second microlocalization and stabilization of damped wave equations on tori.- 4 A few remarks on hyperbolic systems with Zygmund in time coefficients.- 5 Well posedness of linearized Taylor equations in magnetohydrodynamics.- 6 Strictly dissipative non uniqueness with corners.- 7 On the solvability of certain degenerate partial differential operators.- 8 Location and Weyl formula for the eigenvalues of some non self-adjoint operators.- 9 A microscopic point of view on singularities in fluid models.- 10 Geometric optics for Rayleigh pulses in nonlinear elasticity.- 11 Recent results on stability of planar detonations.